Question

Из двух городов А и В, расстояние между которыми равно 87 км, одновременно выехали две автомашины. Скорость первой машины равна 87 км/ч, а скорость второй машины 58 км/ч. На каком расстоянии от города В первая машина догонит вторую и через какое время? Ответ: первая машина догонит вторую на расстоянии … км от города В, и это случится через … часа.

Answer 1

Ответ:

Первая машина догонит вторую на расстоянии 165,3 км от города В, и это случится через 2,9 часа

Answer 2

Problem Analysis

We are given two cities, A and B, with a distance of 87 km between them. Two cars simultaneously start from these cities. The speed of the first car is 87 km/h, and the speed of the second car is 58 km/h. We need to determine at what distance from city B the first car will catch up to the second car and how much time it will take.

Solution

To solve this problem, we can use the formula:

Time = Distance / Speed

Let's calculate the time it takes for the first car to catch up to the second car.

The relative speed of the first car with respect to the second car is the difference between their speeds:

Relative Speed = Speed of First Car - Speed of Second Car

Substituting the given values:

Relative Speed = 87 km/h - 58 km/h = 29 km/h

Now, we can calculate the time it takes for the first car to catch up to the second car:

Time = Distance / Relative Speed

Substituting the given distance of 87 km:

Time = 87 km / 29 km/h = 3 hours

Therefore, the first car will catch up to the second car after 3 hours.

To find the distance from city B where the first car catches up to the second car, we can multiply the time by the speed of the second car:

Distance = Time * Speed of Second Car

Substituting the calculated time of 3 hours and the speed of the second car of 58 km/h:

Distance = 3 hours * 58 km/h = 174 km

Therefore, the first car will catch up to the second car at a distance of 174 km from city B.

Answer

The first car will catch up to the second car at a distance of 174 km from city B, and this will happen after 3 hours.

Please let me know if you need any further assistance.